Find a, b such that 7.2, a, b, 3 are in A. P.

a = 5.8 b = 4.4

Step-by-step explanation:

As

7.2, a, b, 3 are in A. P

As we know common difference of the arithmetic sequence is the difference between the successive term and its preceding term, which is always constant

so

a - 7.2 = b - a

a + a = b + 7.2

2a = b + 7.2

b = 2a - 7.2

also

a, b, 3 are in A. P

b - a = 3 - b

b + b = 3 + a

2b = 3 + a

Putting b = 2a - 7.2 in the equation 2b = 3 + a to find the value of 'a'.

2b = 3 + a

2 (2a - 7.2) = 3 + a

4a - 14.4 = 3 + a

3a = 3 + 14.4

3a = 17.4

Dividing the equation by 3

3a : 3 = 17.4 : 3

a = 5.8

Putting a = 5.8 in the equation b = 2a - 7.2

b = 2a - 7.2

= 2 (5.8) - 7.2

= 11.6 - 7.2

b = 4.4

Therefore,

a = 5.8 b = 4.4